If you do this with the cell under a proper load, say 0.5C-1.5C, this should not damage the cell. I do not know what the LV protection is set at (maybe the spec sheet will tell you that). It should be set at a figure where the cell will recover to >3.0V resting (i.e. not under load).
However if you run the cell down with only a very light load, there will be no voltage sag, so the cell may not recover to >3.0V and in this case it will be damaged.
If you do not already have a good DMM, you should consider getting one, to measure the voltage before and after use / before and after charge.
Please let us know if it fails to cut off, or if the figure is too low.
I would just add that Ultrafire cells in general are poorly regarded for their unreliability and inconsistency.